Some Definitions of Subjunctive Implication, of Counterfactual Implication, and of RelatedConcepts by Rolf Schock; A Note on Subjunctive and Counterfactual Implication by RolfSchockReview by: Arnold KoslowThe Journal of Symbolic Logic, Vol. 35, No. 2 (Jun., 1970), p. 319Published by: Association for Symbolic LogicStable URL: http://www.jstor.org/stable/2270527 .

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REVIEWS 319

ROLF SCHOCK. Some definitions of subjunctive implication, of counterfactual implication, and of related concepts. Notre Dame journal offormal logic, vol. 2 (1961), pp. 206-221.

ROLF SCHOCK. A note on subjunctive and counterfactual implication. Ibid., vol. 3 (1962), pp. 289-290.

The author intends to make explicit the relation between statements in true subjunctive conditionals. His only detailed example of a conditional which his analysis certifies as a sub- junctive conditional is "if triangles were squares, then triangles would have four sides."

After thirty preliminary definitions it is stated that if K and L are sets of formulas, P is a deductive pair, and f is a formula, then K subjunctively implies f by P on the basis of L, if and only if the union of K and L implies f by P. The formulas he refers to are those of the predicate calculus with identity; by a deductive pair P is meant an ordered pair of sets, <P1 , P2> the first of which is a set of formulas, and the second, a set of inference rules. Further, K implies f by P if and only if f is in the smallest class which includes K, includes P1 , and is closed under the rules of P2. The author shows that the conditional mentioned above is a subjunctive conditional if K is the set whose only member is "all squares are four-sided," L contains only "all triangles are squares" as a member, f is the sentence "all triangles are four-sided," P1 is the set of what the author calls the standard set of provable formulas, and P2 has only modus ponens as member.

This characterization of subjunctive implication (relativized to K, L, and P) places no con- straints on the kind of statements which may belong to any one of the relevant classes, and, as the author remarks, quite correctly, his analysis may prove to be too arbitrary for many philosophers.

An attempt is made to place certain restrictions on K and L-that they consist only of true and false statements, respectively. The theory is extended to include five constants, N, S, C, E, and F (intuitively: " necessity," " subjunctively implies," " counterfactually implies," " is em- pirically significant," "is a fact"), and a truth-predicate is defined. However, despite the various versions of subjunctive implication which are presented, there is no application of all this apparatus to any of the hard examples which plague the literature (e.g. XXV 250, XIV 184). Further, if it is true, as one suspects it may be, that the sentences of K will also have to be law- like and not merely true, then it must be noted that not one of the sixty definitions of this paper provides a characterization of "law-like statement" for a first-order theory with identity.

The second article contains corrections to the first article. ARNOLD KOSLOW

ROLF SCHOCK. A definition of event and some of its applications. Theoria (Lund), vol. 28 (1962), pp. 250-268.

This paper begins with some brief comment on the importance of the notion of event for philosophy and science. Given a non-empty domain d, the notion of an event relative to a domain d is defined so that it is essentially a formula of a first-order theory with identity whose individual constants are the members of d, and whose predicates are among the subsets of finite Cartesian products of d with itself.

The author defines what he terms a causal relation whereby a class K of events (for d), causes an event (for d), by C, a causal system (for d), if and only if e is in the smallest class which includes K, includes C1 , and is closed under C2 , where the last two classes are explained as follows: C is the ordered pair <C1, C2> where C1 is a set of events for d, and C2 is a set of rules of causation for d. " Rule of causation for d" is defined in a way which is formally analo- gous to the author's definition of "rule of inference" in a previous paper on subjunctive implication (see preceding review). In fact there is a formal similarity between the relation of subjunctive implication defined in that paper, and the causal relation under discussion.

The so-called rules of causation are construed so generally that the author allows quantifi- cation theory to count as a causal system. To reduce the generality, certain events-"those which actually occur in d"-are singled out with the aid of a notion of satisfaction in d. How- ever, those scientists and philosophers who regard events as bounded portions of space-time will find little sense in speaking of the occurrence of bounded regions of space-time. Further, the fact that in many scientific and philosophical contexts the notion of event has some connection with change, is unreflected in any of the multitude of definitions in this paper.

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